Question

find the zeroes of the following polynomal and verify the relationship between the zeroes and the coefficients of the polynomial
a)4x^2-3x+1
​

Answer 1

Let f(x)=4x

2

−3x−1

Splitting the middle term, we get

=4x

2

−4x+1x−1

=4x(x−1)+1(x−1)

=(x−1)(4x+1)

For f(x)=0, we have

4x

2

−3x−1=0

or (x−1)(4x+1)=0

Either x−1=0⇒x=1

or 4x+1=0

⇒4x=−1

⇒x=

4

−1

∴ The zeroes of f(x) are 1 and

4

−1

.

Verification:

α=1,β=

4

−1

a=4,b=−3 and c=−1

∴α+β=

a

−b

⇒1−

4

1

=

4

−(−3)

⇒

4

3

=

4

3

⇒LHS=RHS

Hence, verified

α.β=

a

c

⇒1×(

4

−1

)=

4

−1

⇒

4

−1

=

4

−1

⇒LHS=RHS

Hence, verified

Answer 2

Answer:

■Given: -

4x^2-3x+1=0

To prove: -

The rootsof the quadratic equation

Proof:-

4x^2-3x+1

=4x^2-4x+1x-1

=4x (x-1)+1(x-1)

= 4x+1=0 or x-1=0

x=-1/4 x=1.

Therefore,

x=-1/4 and x=1 is the root of the quadratic equation.

Hope it helps u mate,

Thank you.